Ajer was born in Norway and started his career with Raelingen FK. When he was 11, he moved to Lillestrm.

In 2014, he signed his first professional contract with IK Start. He made his debut in July of that year. He became the Tippeligaen’s youngest player to serve as team captain at the age of 16.

Ajer left Celtic after making 176 appearances and scoring six goals, and he signed with Premier League Brentford in July 2021. After agreeing to a five-year contract, he made his full debut against Arsenal on the first day of the 21–22 season, winning 2-0.